What are all the ways spacetiime can be distorted/warped? What is formula 4 time dialation?

Question

What are the formulas of spacetime distortion/warpage?
eg: time dialation (gravity and speed), gravity/mass

Answer 1

http://en.wikipedia.org/wiki/Gravitational_time_dilation
all i know of is high speed and gravity distort time. like the gravity of the earth creates a small distortion around it.

Answer 2

gp4rts basically has it right. To expand a bit, in terms of just the time dilation caused by having some relative speed, the first formula (from Einstein's special relativity) is correct. But to put together gravity and relative speed in arbitrarily complicated situations, you need to use the equations of general relativity, which gp4rts wrote down (G = k*T, etc...). This actually comes down to, if I recall correctly, 10 coupled nonlinear differential equations (e.g. it's very, very complicated).

However, Einstein did derive an expression for the time dilation between two observers in a constant gravitational field, one [we'll call him the primed observer] a height h above the other. This expression is t = t' (1 - gh/(c^2) ) where g is the acceleration due to gravity, h is the height, and c is the speed of light. Now, if h is large enough that the g at the bottom is not the g at the top, this won't be right. An approximate expression can be gotten to be t = t' ( 1 - GM / ( r * c^2 ) ) where G is the gravitational constant, M is the mass of the body causing the gravitational field, and r is the radius from the center of M that the unprimed observer is at. This is valid when GM/(r*c^2) is much less than one, and can be derived without the full theory of general relativity. When that's not true, the expression becomes (and this is something that you can only get from going through general relativity) t = t' * sqrt( 1 - 2GM / ( r * c^2 ) ). The basic difference in uses is that the first equation can only be used when gravity is weak (in the physical sense... a black hole or neutron star has strong gravity in this sense, the Earth has weak gravity).

Answer 3

Spacetime is distorted by masses and energy. The formula for time dilation is t = t'/√[1-v^2/c^2], where t is the time observed by the (relatively) stationary observer of events occuring in time t' in an inertial frame moving at velocity v. c is the speed of lght.

The formula for spacetime distortion is G_uv = K*T_uv, where G_uv is the Einstein Tensor and T_uv is the stress-energy tensor, K=8πG/c^4, where G=Newtonian gravitational constant. Good luck in computing those tensors,

Answer 4

Gravity is the only thing.

The equation you want (in geometrized units) is:

Gab = 8piTab

Gab is the Einstein tensor Gab = Rab - 1/2 Rgab
(where Rab is the Ricci tensor, R the Ricci scalar and gab the metric tensor).
Tab is the stress energy tensor.

Its all a bit scary really isn't it, but what it says is that the shape of space time - described by Gab - is linked directly to the mass and energy in the space, taking account of its movement (i.e. moving mass acts differently to stationary mass0.

The tensors are designed to allow a frame invariant description which is quite unlike the one we use day to day, where we have to use transformations (you may have met these in special relativity, such as the Lorntz transformation).